183_notes:potential_energy

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183_notes:potential_energy [2015/10/06 11:07] – [Potential Energy Depends on Separation NOT Location] caballero183_notes:potential_energy [2021/03/12 02:43] (current) – [What is potential energy?] stumptyl
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 +Section 6.7 in Matter and Interactions (4th edition)
 + 
 ===== Potential Energy ===== ===== Potential Energy =====
  
-For multi-particles systems, you will have to keep track of the energy changes associated with the internal forces. That is, the work done by objects in the system on other objects in the system. As you will read, we can often associate an energy with pairs of interacting of objects, which we call "potential energy." In these notes, you will read about potential energy, how it keeps track of the energy associated with interactions internal to the system, and some of its properties. +For multi-particles systems, you will have to keep track of the energy changes associated with the internal forces. That is, the work done by objects in the system on other objects in the system. As you will read, we can often associate an energy with pairs of interacting of objects, which we call "potential energy." **In these notes, you will read about potential energy, how it keeps track of the energy associated with interactions internal to the system, and some of its properties. 
 +**
 ==== Lecture Video ==== ==== Lecture Video ====
  
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 ==== What is potential energy? ==== ==== What is potential energy? ====
  
-Potential energy is energy associated with pairs of objects that interact with each other within a system. Because potential energy exists between pairs of objects, no single object can have potential energy, it is a multi-particle system that has potential energy. It's referred to as potential energy because it can be converted to other forms of energy. Common examples of systems with potential energy include stretched/compressed springs, galaxies of stars interacting gravitationally, atoms in which protons and electrons interact electrically, and TNT.+__**Potential energy (J)**__ is energy associated with pairs of objects that interact with each other within a system. Because potential energy exists between pairs of objects, no single object can have potential energy, it is a multi-particle system that has potential energy. It's referred to as potential energy because it can be converted to other forms of energy. Common examples of systems with potential energy include stretched/compressed springs, galaxies of stars interacting gravitationally, atoms in which protons and electrons interact electrically, and TNT.
  
 ==== Formal definition of Potential Energy ==== ==== Formal definition of Potential Energy ====
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 $$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2,f} - \vec{r}_{1,f}\right)-\left(\vec{r}_{2,i} - \vec{r}_{1,i}\right)=\vec{r}_f-\vec{r}_i = \Delta \vec{r}$$ $$\Delta\vec{r}_2 - \Delta\vec{r}_1 = \left(\vec{r}_{2,f} - \vec{r}_{1,f}\right)-\left(\vec{r}_{2,i} - \vec{r}_{1,i}\right)=\vec{r}_f-\vec{r}_i = \Delta \vec{r}$$
  
-This is precisely the vector that tracks the change in separation between the two objects.+This is precisely the vector that tracks the change in separation between the two objects, $\Delta \vec{r}$.
  
-$$\Delta U = -\vec{f}_{2,1}\cdot \underbrace{\Delta \vec{r}}$$+$$\Delta U = -\vec{f}_{2,1}\cdot \Delta \vec{r}$$
  
 From this you can conclude that any change in potential energy is associated with a change in the shape of a system. For rigid systems, the potential energy is constant. From this you can conclude that any change in potential energy is associated with a change in the shape of a system. For rigid systems, the potential energy is constant.
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